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Pozar defines the characteristic impedance of a transmission line in terms of the RLGC parameters of the transmission line, and uses the term intrinsic impedance to refer specifically to the relation between the magnitudes of the electric and magnetic fields of a plane wave traveling in an optical medium.
Should this article use the RLGC parameters consistently throughout, perhaps with a statement that the characteristic impedance of a transmission line is analogous to the intrinsic impedance of an optical medium?
Pozar, David (2004). Microwave Engineering (3rd edition ed.). {{
cite book}}
: |edition=
has extra text (
help); Unknown parameter |month=
ignored (
help)
IJW 01:59, 14 September 2006 (UTC)
I have edited the article to define the characteristic impedance in terms of RLGC parameters and linked to Medium (optics) instead of defining characteristic impedance in terms of permittivity and permeability. I also removed the section on frequency dependence because it is misleading; R and G are not constant and the frequency dependence of is not as simple as the previous version of the article stated. At AC and higher frequencies and . Only at very low frequencies (where the thickness of the conductors is comparable to the skin depth) is R relatively constant, but the frequency dependence of G remains. I will revisit this section to include these facts and give a more complete treatment.
IJW 14:41, 14 September 2006 (UTC)
Following is the section on frequency dependence that I deleted:
=== variation with frequency ===
The impedance of a real lossy transmission line is not constant, but varies with frequency. At low frequencies, when
- and ,
the characteristic impedance of a transmission line is
- .
At high frequencies where
- and ,
then the characterstic impedance is
- .
So there are two distinct characteristic impedances for every line. Usually G is very small so the low-frequency impedance is high, whereas the high-frequency impedance is low. The break points in the impedance frequency graph are at and (where ). If , it is obvious that . Between these two break frequencies the cable impedance decreases smoothly.
Example
Take the case of a 50Ω coaxial cable with polyethylene dielectric. R is about 100 mΩ/m and G < 20 pS/m (based on measurements of leakage resistance in a 1 m length). Using , L can be calculated at about 250 nH/m. So,
- ω2 = R/L = 200 krad/s (f2 = 30 kHz)
and
- ω1 = G/C = 0.2 rad/s (f1 = 30 millihertz)
At 100 Hz the 50 ohm coaxial cable will have an impedance of about 900 ohms, only reaching 50 ohms at about 30 or 40 kHz. The phase angle of the impedance between the two break frequencies is leading (the cable looks capacitive).
IJW 17:11, 14 September 2006 (UTC)
As Mebden himself wrote in the page "intrinsic impedance", electrical impedance and electromagnetic impedance should not be confused. The impedance of a transmission line is an electrical impedance and the impedance of a medium is an electromagnetic impedance.
LPFR
08:51, 23 October 2006 (UTC)
Impedance of a transmission line or impedance of an electrical circuit is the ratio of a voltage divided by a current, both of them measurable quantities. Impedance of vacuum or impedance o a substance is something () related to the properties of the substance in an electromagnetic field. It just happened that the units of this value are ohms and people could not avoid calling it "impedance". Impedance of a line and impedance of vacuum are very different things. The difference is still greater if you think of transmission lines built with discrete inductors and capacitors used (in the past) as delay lines.
LPFR
12:05, 1 October 2006 (UTC)
Would it be accurate to add this (e.g. to the introduction): "A high-quality (high conductance) transmission line tends to have a low characteristic impedance, and vice versa." (Or is it the other way around?) -- Coppertwig 13:18, 11 January 2007 (UTC)
Characteristic Impedance? What's infinity got to do with it? ____________________________________________________________ —Preceding unsigned comment added by 92.40.34.110 ( talk) 11:25, 6 September 2009 (UTC)
I wish people would avoid talking about "infinite" lines when discussing Z0. Has anybody ever seen one?
Its true, that Zin of a line is equal to "Z0" multiplying a quotient, containing the hyperbolic tangent of the product of length of the line and the propagation co-efficient (easily derived from the transfer matrix of a line). If you let the length of the line tend to infinity, then the quotient tends to unity and one is left with Zin = Z0. Which is all very well mathematically, but it has never been shown practically, because of the problem of obtaining, for example, an infinite length of 50 ohm coaxial cable!
There is a much better definition of Z0, but which requires knowledge of iterative impedance and image impedance. As follows.
One can always find an impedance which when connected to the output terminals of any two port network (including a transmission line), that will give the same impedance, measured at the input terminals. This is called the "iterative impedance" of the network Zit1. Similarly one can always find a suitable generator, whose source impedance, when placed at the input terminals of a two port network will give the same impedance, measured at the output terminals of the network. This is also an iterative impedance, Zit2.
If the network is symmetrical, i.e the determinant of the transfer matrix is unity, then Zit1 = Zit2 = Zit.
Similarly the "image impedance" of a two port network, is that input impedance (and is the complex conjugate)of the generator source impedance, due to a load at the output terminals, and causes maximum power to be transferred from the generator to the network, Zim1. Similarly if the output impedance of the network is equal to (and is the complex conjugate of) the load impedance, then maximum power will be transferred from the network to the load, Zim2. For a symmetrical network, Zim1 = Zim2 = Zim.
And now for the definition. If (and only if) for a symmetrical network, the case that the "iterative impedance" is equal to the "image impedance", this is known as the "characteristic impedance" of the network, and is given the symbol Z0. Z0 = Zim = Zit.
Note, it doesn't matter if the network is a piece of coax cable a mile long, or three resistors connected in a "T" configuration, the definition is still the same. This is charactersitic impedance, and doesn't require the mention of the word infinity.
Phil Robinson —Preceding unsigned comment added by 92.40.34.110 ( talk) 11:09, 6 September 2009 (UTC)
"Do any reliable sources use your definition?"
Yes see "Advanced Electrical Engineering" by AH Morton Phil Robinson — Preceding unsigned comment added by 94.72.252.35 ( talk) 11:24, 20 October 2016 (UTC)
This impedance, remains the same, no matter how long the line is, because the ratio of voltage applied to the current, remains the same, but their actual values reduce, along the length, of a lossy line.
Is the above statement false?, please tell me how to correct it, is the one below better?
This impedance, remains the same, no matter how far along a uniform line, you measure it, because the ratio of voltage applied to the current, remains the same, but their actual values reduce, along the length of a lossy line.
or
This impedance, remains the same, no matter how long the line is, even if it is infinite, because the ratio of voltage applied to the current, remains the same, but their actual values reduce, along the length, of a lossy line.
Bookbuddi ( talk) 17:05, 15 April 2012 (UTC)
I am trying to give a practical example of what happens with real non infinite lines (to make the concept easier to understand, as we don't have any infinite lines to measure).
so can I say:
On a real, non-infinite terminated line, we can see that the impedance remains the same, no matter how far along the line you measure it, because the ratio of voltage applied to the current remains the same, but their actual values reduce, along the length of a lossy line. Bookbuddi ( talk) 19:32, 15 April 2012 (UTC)
Zolot, the characteristic impedance of a lossless transmission line is real, i.e., resistive. For example:
I know this is splitting hairs, but this article probably needs to address the differences between Characteristic Impedance and Surge Impedance. I have numerous references, but the basic reference to trigger some thought is the IEEE-STD-100-1984, IEEE Standard Dictionary of Electrical and Electronics Terms. [1] On page 136 we find...
Characteristic Impedance
(1)Data transmission
(1.A) Two-conductor transmission line for a traveling transverse electromagnetic wave
(1.B) Coaxial transmission line
[. . .]
(6)Surge Impedance
Then on page 904 we have the standalone definition of surge impedance...
Surge impedance (self-surge impedance)
The first sentence in this article suggests characteristic impedance and surge impedance are the same, but they have separate definitions for a reason. Few in the RF industry would be confused, but if the IEEE makes a distinction so should we I propose. Crcwiki ( talk) 18:06, 28 September 2015 (UTC)
References
{{
cite book}}
: Check |isbn=
value: length (
help); Unknown parameter |ignore-isbn-error=
ignored (|isbn=
suggested) (
help)
I thought that the section on the lossless line could use some context for why lossless lines are considered during transmission line analysis. I added some motivation behind the lossless line model, and discussed some implications of analyzing lossless lines. Prayerfortheworld ( talk) 08:57, 8 December 2015 (UTC)
" It can be shown that an equivalent definition is: the characteristic impedance of a line is that impedance which when terminating an arbitrary length of line at its output will produce an input impedance equal to the characteristic impedance."
I'm not sure the sentence's logic can be followed - it seems circular, in the end using "characteristic impedance" itself to define "characteristic impedance". If there is logic (that I cannot see), perhaps it can be reworded?
Mike ( talk) 17:44, 1 February 2016 (UTC)
The comment(s) below were originally left at Talk:Characteristic impedance/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
I don't see a reason why this page cannot be unified with the page dealing with "wave impedance"
|
Last edited at 19:35, 16 November 2012 (UTC). Substituted at 11:16, 29 April 2016 (UTC)
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Constant314, regarding your last undo you may be right, so I just want to understand. Consider the following scenario: you have a transmission line opened at one end, and you apply a single pulse at the other extremity. Before the pulse has reached the opened end, you measure the current I and voltage V at some point. The ratio V/I is the characteristic impedance. So far so good. Now, you repeat the same experience but with a constant DC voltage of 1V applied together with the pulse (meaning you have to apply the DC voltage before the pulse and wait some time the voltage stabilises). Since the line is opened, the DC voltage causes no DC current to flow, and the characteristic impedance you measure is now (V+1)/I. Isn't it a contradiction? maimonid ( talk) 11:34, 22 January 2018 (UTC)
Constant314: OK for the maths but this was not the point. I now understand what has confused you in my previous contribution. I hope you will also understand my point of view. Let me express it in the following way. I suggest to replace the sentence:
The table of practical examples cites an NXP app note which references an Intel motherboard reference for designing the impedance of traces.
These are inconsistent with the specification. For example, HDMI according to spec v1.3a (which is freely available to download but you have to register) says the "cable area" should have 100 ohms +/- 10%, not 95 ohm +/-15%.
The subtlety here is that Intel has published some papers which indicate that emperically, designing a motherboard with a slightly lower impedance than specification can lead to improved performance (see "Improve Storage IO Performance by Using 85Ohm Package and Motherboard Routing, https://ieeexplore.ieee.org/document/5642794). However, the table is unclear on the fact that the specification actually calls for 100 ohms.
i would suggest revising the table to have an extra column: one for spec number, one for recommended PCB/package design. It's helpful to have both on hand. But as the table is, if it's meant to portray the actual committee-approved spec for impedance of the standards, it's wrong. — Preceding unsigned comment added by 132.147.66.42 ( talk) 07:48, 5 October 2018 (UTC)
I reviewed the previous relevant talk.
Is not correct because it is true regardless of reflections. By saying it is the ratio of a wave traveling in one direction automatically removes the effect of a reverse wave. The presence of a reverse wave has no effect on the forward wave. The net voltage and current, however, are another story as I assume everyone understands. In fact, a wave can ONLY travel in one direction, so it even seems redundant to say so; other than to say "traveling in either direction". It would be in full:
Comments? -- Steve -- ( talk) 01:10, 17 June 2019 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 |
Pozar defines the characteristic impedance of a transmission line in terms of the RLGC parameters of the transmission line, and uses the term intrinsic impedance to refer specifically to the relation between the magnitudes of the electric and magnetic fields of a plane wave traveling in an optical medium.
Should this article use the RLGC parameters consistently throughout, perhaps with a statement that the characteristic impedance of a transmission line is analogous to the intrinsic impedance of an optical medium?
Pozar, David (2004). Microwave Engineering (3rd edition ed.). {{
cite book}}
: |edition=
has extra text (
help); Unknown parameter |month=
ignored (
help)
IJW 01:59, 14 September 2006 (UTC)
I have edited the article to define the characteristic impedance in terms of RLGC parameters and linked to Medium (optics) instead of defining characteristic impedance in terms of permittivity and permeability. I also removed the section on frequency dependence because it is misleading; R and G are not constant and the frequency dependence of is not as simple as the previous version of the article stated. At AC and higher frequencies and . Only at very low frequencies (where the thickness of the conductors is comparable to the skin depth) is R relatively constant, but the frequency dependence of G remains. I will revisit this section to include these facts and give a more complete treatment.
IJW 14:41, 14 September 2006 (UTC)
Following is the section on frequency dependence that I deleted:
=== variation with frequency ===
The impedance of a real lossy transmission line is not constant, but varies with frequency. At low frequencies, when
- and ,
the characteristic impedance of a transmission line is
- .
At high frequencies where
- and ,
then the characterstic impedance is
- .
So there are two distinct characteristic impedances for every line. Usually G is very small so the low-frequency impedance is high, whereas the high-frequency impedance is low. The break points in the impedance frequency graph are at and (where ). If , it is obvious that . Between these two break frequencies the cable impedance decreases smoothly.
Example
Take the case of a 50Ω coaxial cable with polyethylene dielectric. R is about 100 mΩ/m and G < 20 pS/m (based on measurements of leakage resistance in a 1 m length). Using , L can be calculated at about 250 nH/m. So,
- ω2 = R/L = 200 krad/s (f2 = 30 kHz)
and
- ω1 = G/C = 0.2 rad/s (f1 = 30 millihertz)
At 100 Hz the 50 ohm coaxial cable will have an impedance of about 900 ohms, only reaching 50 ohms at about 30 or 40 kHz. The phase angle of the impedance between the two break frequencies is leading (the cable looks capacitive).
IJW 17:11, 14 September 2006 (UTC)
As Mebden himself wrote in the page "intrinsic impedance", electrical impedance and electromagnetic impedance should not be confused. The impedance of a transmission line is an electrical impedance and the impedance of a medium is an electromagnetic impedance.
LPFR
08:51, 23 October 2006 (UTC)
Impedance of a transmission line or impedance of an electrical circuit is the ratio of a voltage divided by a current, both of them measurable quantities. Impedance of vacuum or impedance o a substance is something () related to the properties of the substance in an electromagnetic field. It just happened that the units of this value are ohms and people could not avoid calling it "impedance". Impedance of a line and impedance of vacuum are very different things. The difference is still greater if you think of transmission lines built with discrete inductors and capacitors used (in the past) as delay lines.
LPFR
12:05, 1 October 2006 (UTC)
Would it be accurate to add this (e.g. to the introduction): "A high-quality (high conductance) transmission line tends to have a low characteristic impedance, and vice versa." (Or is it the other way around?) -- Coppertwig 13:18, 11 January 2007 (UTC)
Characteristic Impedance? What's infinity got to do with it? ____________________________________________________________ —Preceding unsigned comment added by 92.40.34.110 ( talk) 11:25, 6 September 2009 (UTC)
I wish people would avoid talking about "infinite" lines when discussing Z0. Has anybody ever seen one?
Its true, that Zin of a line is equal to "Z0" multiplying a quotient, containing the hyperbolic tangent of the product of length of the line and the propagation co-efficient (easily derived from the transfer matrix of a line). If you let the length of the line tend to infinity, then the quotient tends to unity and one is left with Zin = Z0. Which is all very well mathematically, but it has never been shown practically, because of the problem of obtaining, for example, an infinite length of 50 ohm coaxial cable!
There is a much better definition of Z0, but which requires knowledge of iterative impedance and image impedance. As follows.
One can always find an impedance which when connected to the output terminals of any two port network (including a transmission line), that will give the same impedance, measured at the input terminals. This is called the "iterative impedance" of the network Zit1. Similarly one can always find a suitable generator, whose source impedance, when placed at the input terminals of a two port network will give the same impedance, measured at the output terminals of the network. This is also an iterative impedance, Zit2.
If the network is symmetrical, i.e the determinant of the transfer matrix is unity, then Zit1 = Zit2 = Zit.
Similarly the "image impedance" of a two port network, is that input impedance (and is the complex conjugate)of the generator source impedance, due to a load at the output terminals, and causes maximum power to be transferred from the generator to the network, Zim1. Similarly if the output impedance of the network is equal to (and is the complex conjugate of) the load impedance, then maximum power will be transferred from the network to the load, Zim2. For a symmetrical network, Zim1 = Zim2 = Zim.
And now for the definition. If (and only if) for a symmetrical network, the case that the "iterative impedance" is equal to the "image impedance", this is known as the "characteristic impedance" of the network, and is given the symbol Z0. Z0 = Zim = Zit.
Note, it doesn't matter if the network is a piece of coax cable a mile long, or three resistors connected in a "T" configuration, the definition is still the same. This is charactersitic impedance, and doesn't require the mention of the word infinity.
Phil Robinson —Preceding unsigned comment added by 92.40.34.110 ( talk) 11:09, 6 September 2009 (UTC)
"Do any reliable sources use your definition?"
Yes see "Advanced Electrical Engineering" by AH Morton Phil Robinson — Preceding unsigned comment added by 94.72.252.35 ( talk) 11:24, 20 October 2016 (UTC)
This impedance, remains the same, no matter how long the line is, because the ratio of voltage applied to the current, remains the same, but their actual values reduce, along the length, of a lossy line.
Is the above statement false?, please tell me how to correct it, is the one below better?
This impedance, remains the same, no matter how far along a uniform line, you measure it, because the ratio of voltage applied to the current, remains the same, but their actual values reduce, along the length of a lossy line.
or
This impedance, remains the same, no matter how long the line is, even if it is infinite, because the ratio of voltage applied to the current, remains the same, but their actual values reduce, along the length, of a lossy line.
Bookbuddi ( talk) 17:05, 15 April 2012 (UTC)
I am trying to give a practical example of what happens with real non infinite lines (to make the concept easier to understand, as we don't have any infinite lines to measure).
so can I say:
On a real, non-infinite terminated line, we can see that the impedance remains the same, no matter how far along the line you measure it, because the ratio of voltage applied to the current remains the same, but their actual values reduce, along the length of a lossy line. Bookbuddi ( talk) 19:32, 15 April 2012 (UTC)
Zolot, the characteristic impedance of a lossless transmission line is real, i.e., resistive. For example:
I know this is splitting hairs, but this article probably needs to address the differences between Characteristic Impedance and Surge Impedance. I have numerous references, but the basic reference to trigger some thought is the IEEE-STD-100-1984, IEEE Standard Dictionary of Electrical and Electronics Terms. [1] On page 136 we find...
Characteristic Impedance
(1)Data transmission
(1.A) Two-conductor transmission line for a traveling transverse electromagnetic wave
(1.B) Coaxial transmission line
[. . .]
(6)Surge Impedance
Then on page 904 we have the standalone definition of surge impedance...
Surge impedance (self-surge impedance)
The first sentence in this article suggests characteristic impedance and surge impedance are the same, but they have separate definitions for a reason. Few in the RF industry would be confused, but if the IEEE makes a distinction so should we I propose. Crcwiki ( talk) 18:06, 28 September 2015 (UTC)
References
{{
cite book}}
: Check |isbn=
value: length (
help); Unknown parameter |ignore-isbn-error=
ignored (|isbn=
suggested) (
help)
I thought that the section on the lossless line could use some context for why lossless lines are considered during transmission line analysis. I added some motivation behind the lossless line model, and discussed some implications of analyzing lossless lines. Prayerfortheworld ( talk) 08:57, 8 December 2015 (UTC)
" It can be shown that an equivalent definition is: the characteristic impedance of a line is that impedance which when terminating an arbitrary length of line at its output will produce an input impedance equal to the characteristic impedance."
I'm not sure the sentence's logic can be followed - it seems circular, in the end using "characteristic impedance" itself to define "characteristic impedance". If there is logic (that I cannot see), perhaps it can be reworded?
Mike ( talk) 17:44, 1 February 2016 (UTC)
The comment(s) below were originally left at Talk:Characteristic impedance/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
I don't see a reason why this page cannot be unified with the page dealing with "wave impedance"
|
Last edited at 19:35, 16 November 2012 (UTC). Substituted at 11:16, 29 April 2016 (UTC)
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Constant314, regarding your last undo you may be right, so I just want to understand. Consider the following scenario: you have a transmission line opened at one end, and you apply a single pulse at the other extremity. Before the pulse has reached the opened end, you measure the current I and voltage V at some point. The ratio V/I is the characteristic impedance. So far so good. Now, you repeat the same experience but with a constant DC voltage of 1V applied together with the pulse (meaning you have to apply the DC voltage before the pulse and wait some time the voltage stabilises). Since the line is opened, the DC voltage causes no DC current to flow, and the characteristic impedance you measure is now (V+1)/I. Isn't it a contradiction? maimonid ( talk) 11:34, 22 January 2018 (UTC)
Constant314: OK for the maths but this was not the point. I now understand what has confused you in my previous contribution. I hope you will also understand my point of view. Let me express it in the following way. I suggest to replace the sentence:
The table of practical examples cites an NXP app note which references an Intel motherboard reference for designing the impedance of traces.
These are inconsistent with the specification. For example, HDMI according to spec v1.3a (which is freely available to download but you have to register) says the "cable area" should have 100 ohms +/- 10%, not 95 ohm +/-15%.
The subtlety here is that Intel has published some papers which indicate that emperically, designing a motherboard with a slightly lower impedance than specification can lead to improved performance (see "Improve Storage IO Performance by Using 85Ohm Package and Motherboard Routing, https://ieeexplore.ieee.org/document/5642794). However, the table is unclear on the fact that the specification actually calls for 100 ohms.
i would suggest revising the table to have an extra column: one for spec number, one for recommended PCB/package design. It's helpful to have both on hand. But as the table is, if it's meant to portray the actual committee-approved spec for impedance of the standards, it's wrong. — Preceding unsigned comment added by 132.147.66.42 ( talk) 07:48, 5 October 2018 (UTC)
I reviewed the previous relevant talk.
Is not correct because it is true regardless of reflections. By saying it is the ratio of a wave traveling in one direction automatically removes the effect of a reverse wave. The presence of a reverse wave has no effect on the forward wave. The net voltage and current, however, are another story as I assume everyone understands. In fact, a wave can ONLY travel in one direction, so it even seems redundant to say so; other than to say "traveling in either direction". It would be in full:
Comments? -- Steve -- ( talk) 01:10, 17 June 2019 (UTC)